2 Answers

1 vote

(27/8)^-(2/3). First consider that the power is negative: This means that you need the reciprocal of the fraction.
So (27/8)^-(2/3) = (8/27)^(2/3)
If you consider the fractional power, then it can be written as
(2/3)=(1/3)*(2)
Going to the laws of indices, 'powers outside the brackets always multiply'
So (8/27)^(2/3) = [(8/27)^(1/3)]^2
You can cube root the denominator and numerator separately, giving
(8/27)^(1/3) = (2/3)
So [(8/27)^(1/3)]^2 = (2/3)^2
You can then square the denominator and the numerator
So (2/3)^2 = 4/9
Which is your answer :) [Hopefully]

its fractional indices but this is a negative so you need to do the recipricol: 8/27 ^2/3 and then you use the denominator which is three so therefore find the cubed root of the numbers after that you use the numerator which is two and you square the numbers. the answer is 4/9